Now you should have two keys: a public key at ~/.ssh/id_rsa.pub and a corresponding private key at ~/.ssh/id_rsa. Do not share your private key with anybody. Your public key can be copied to any remote account that supports SSH and you will be able to use your private key to authenticate with it.

E.g. copy your public key to your LUG@UCLA account:

$ ssh-copy-id user@ssh.linux.ucla.edu

Consider using ssh-agent so you don't have to type your passphrase every time you use your private key. In most modern desktop environments (e.g. GNOME, KDE) this is handled in a GUI pop-up when you first use your private key.

Type man ssh-keygen, man ssh-copy-id, or man ssh-agent to see the complete manuals for these tools.